## Problem Description and Symbolic Representation

The problem involves minimizing the cost of producing standing desks and office chairs using a special machine, subject to certain constraints.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ = number of standing desks
- $x_2$ = number of office chairs

The objective function to minimize is the total cost:
- $500x_1 + 230x_2$

The constraints are:
1. Machine operation time: $60x_1 + 35x_2 \geq 2000$
2. Minimum total items: $x_1 + x_2 \geq 100$
3. Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'standing desks'), ('x2', 'office chairs')],
    'objective_function': '500*x1 + 230*x2',
    'constraints': [
        '60*x1 + 35*x2 >= 2000',
        'x1 + x2 >= 100',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("StandingDesks_OfficeChairs")

# Define the variables
x1 = model.addVar(name="standing_desks", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="office_chairs", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: minimize cost
model.setObjective(500*x1 + 230*x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(60*x1 + 35*x2 >= 2000, name="machine_time")
model.addConstr(x1 + x2 >= 100, name="min_items")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Standing Desks: {x1.varValue}")
    print(f"Office Chairs: {x2.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```